Question: Find the distance between the points (6, -2) and (-7, 4). {1} {2} {3} {4} {5} {6} {7} {8} {9} {10} {\llap{-}2} {\llap{-}3} {\llap{-}4} {\llap{-}5} {\llap{-}6} {\llap{-}7} {\llap{-}8} {\llap{-}9} {\llap{-}10} {1} {2} {3} {4} {5} {6} {7} {8} {9} {10} {\llap{-}2} {\llap{-}3} {\llap{-}4} {\llap{-}5} {\llap{-}6} {\llap{-}7} {\llap{-}8} {\llap{-}9} {\llap{-}10} (6, -2) (-7, 4) $13$ $6$
Change in $x$ (-7) 13 Change in $y$ (-2) The distance is the length of the hypotenuse of this right triangle. By the Pythagorean Theorem, that length is equal to: $\sqrt{13^2 + 6^2}$ $= \sqrt{205}$